Arc Forumnew | comments | leaders | submitlogin
Pursuing higher quasiquotation (
4 points by rocketnia 1599 days ago | 5 comments

4 points by rocketnia 1599 days ago | link

To summarize this post, I'm trying to generalize macros and quasiquotation in several ways all at once, but most of the hard problems I'm encountering center on an idea I call "higher quasiquotation":

- A quasiquotation is data shaped like an s-expression with s-expression-shaped holes.

- A quasiquotation of higher degree is data shaped like a quasiquotation with quasiquotation-shaped holes.

I already want to define macros whose bodies are not s-expressions but quasiquotations, so I already want to move up one degree on this progression. To make sure this design is correct, I want it to work even if I move up an arbitrary number of degrees. If it works, I expect one macro system to work for quasiquotation macros, regular macros, and reader macros, all in the same generalized way.

But... it's not working yet. :)


4 points by conanite 1598 days ago | link

Is a higher quasiquotation like a nested macro? A macro that generates macros? Like (made-up example) ...

    (mac metamac (opname op)
      `(mac ,opname (name n)
         `(mac ,name (x)
            `(',',,op ,,n ,x))))

    (metamac multiplier *) ;; defines a macro called multiplier

    (multiplier times-five 5) ;; defines a macro called times-five

    (times-five 3) ;; expands to (* 5 3)
Or something else?


3 points by rocketnia 1596 days ago | link

No, just like you can nest parentheses without spontaneously having quasiquotation, you can nest quasiquotations like you're talking about without reaching a higher degree of quasiquotation.

Suppose we have notations like so:

  ( ) parentheses
  ` , quasiquotation
  ^ $ the next higher degree of quasiquotation
      (I would go on, but I'll run out of punctuation.)
S-expressions are bounded on both sides by single characters, and they nest within each other like this (labeling the layers as "a" and "b" and anything outside their lexical extent as "__"):

  (a (b) a) --
If we want to look at just the "b" s-expression, it's simple to write that down on its own:

Quasiquotations are bounded on both sides by s-expressions, and they nest like this:

  `(a `(b ,(a ,(--) a) (b) b) a ,(--) a (a) a) --
The meaning of "--" in the inner expressions hasn't changed: Every "--" is outside the lexical boundary of the `(a ...) quasiquotation, just as every "a" is outside the lexical extent of the `(b ...) quasiquotation. Occurrences of "--" can appear when the lexical extent closes on an s-expression (")") or a quasiquotation (","), and both of these are shown in the example.

We can isolate the "b" part pretty easily again, but we need to allow for holes in our data structure:

  `(b ,(--) (b) b)
Quasiquotations of the next higher degree are bounded on both sides by quasiquotations, and they nest like this:

              a ,(b (b) b) a ,(b) a `(a) a (a) a)
          b ,(a) b `(b) b (b) b)
      a ,(--) a `(a) a (a) a)
Occurrences of "--" can appear when the lexical extent closes on an s-expression (")"), a quasiquotation (","), or a quasiquotation of the next higher degree ("$"), and all of these are shown in the example.

This time, writing down just the "b" part gets tricky using s-expression-shaped syntax because one of the holes has orphaned sections inside (holes in the hole):

      $`(-- ,(b (b) b) ,(b))
      b ,(--) b `(b) b (b) b)
When we have more than one orphaned section in the same hole like we do here, we may need to use labels (or positions, or extra hole structure) to tell them apart so we can insert the "b" section into the "a" section deterministically. So far I haven't figured out how to represent this data in a way that works, let alone an elegant way.

For a concrete use case, look at it this way: When do we use ( and )? When our DSLs don't last all the way to the end of the file. When do we use ` and ,? When our DSLs have holes in them (although it might be unusual to hear this, because most Lisps couple these syntaxes together with a particular nested-list-generating DSL). When do we use ^ and $? When our DSLs have holes with holes in them. And so on, where higher degrees of quasiquotation have more and more intricate holes.

Let's say I'm writing a macro that implements a DSL where Common Lisp code and Arc code can be combined in the same function. (I'm going with Common Lisp so that we can't simply compile it to inline Racket code.) I may have Common Lisp s-expressions occurring under my Arc s-expressions and Arc s-expressions occurring under my Common Lisp s-expressions, but I want Arc variables to be visible in all the Arc parts and Common Lisp variables to be visible in all the Common Lisp parts. When we take a look at the lexical scope of any one local Common Lisp (or Arc) variable in that code, it's not simply shaped like an s-expression like traditional lexical scopes are; it has holes-with-holes wherever the Arc (respectively Common Lisp) expressions occur. So ^ and $ are a natural fit for the DSL:

  (def three ()
      ^`(let ((common-lisp-var 1))
          $`(let arc-var 2
              (+ ,common-lisp-var arc-var)))))


3 points by rocketnia 1595 days ago | link

Maybe I could actually use something like that ^ and $ syntax.

I'll need to generalize it to an infinite number of degrees:

  (     )
  ^.    $.
  ^-.   $-.
  ^--.  $--.
  ^---. $---.
Since Scheme's ,',',', technique doesn't generalize to other DSLs, I'll want to have at least one way to unquote from more than one level of nested quasiquotation at once:

Cene has more than one notation for doing that. (I can write a label on an outer layer, and then I can unquote all the way to a particular label.) I'd like to support various unquoting styles as macros, but maybe that macro system can expand to a notation like this, so getting this to work first seems best.

Finally, representing data structures with orphaned parts might be easy enough once I actually try using key-value tables to hold orphans like I've planned.

I think I like this approach even better than the one I reached in the blog post. It means that I actually can process an infinite number of degrees of quasiquotation "in the reader" rather than letting the top level of macroexpansion begin with an s-expression.

But I suppose this and the blog post tackle two different parts of the problem. The blog post's approach/challenges still apply to the process of parsing this syntax into an infinite-degree quasiquotation.


2 points by rocketnia 1590 days ago | link

I've fooled myself before, but I may have settled on the right data structure to represent higher quasiquotations.

I define the data structure three times:

- Once as a sequence of types that represent progressively higher-degree quasiquotations, which use maps to hold orphaned nodes. (

- Once as a single type that can represent arbitrarily high degrees of quasiquotation, but in a very weakly typed way. (

- Once as a sequence of types that represent progressively higher-degree quasiquotations, which use type families to hold orphaned nodes. This is the most strongly typed of all these representations. (

Here's the simplest one, the one in the middle:

  data HDExpr s m
    = HDExprMedia (m (HDExprNonMedia s m))
  data HDExprNonMedia s m
    = HDExprHole s [Map s (HDExpr s m)]
    | HDExprLayer (HDExpr s m) [Map s (HDExpr s m)]
It's not very self-documenting, so to start describing it, here's a Lispier pseudocode:

  <expr> ::= <s-expression where some leaves are <paren>>
  <paren> ::= (close <identifier> <list of <environment of <expr>>>)
  <paren> ::= (open-and-close <expr> <list of <environment of <expr>>>)
I say "s-expression" there, but we could have any monad there for our syntax. If we work in the s-expression monad, the usual quasiquote operations ` , are parens of degree 1. When the monad we're working in is Haskell's (Writer String), our syntax is effectively reader syntax, where the ( ) parens are degree 1 and ` , are degree 2.

(There are also parens of degree 0, but they're a bit weird: Once they open, they only close again by reaching the end of the syntax. So when we're in the s-expression monad, perhaps ' is a paren of degree 0. When we're in the (Writer String) monad, perhaps pressing enter at the end of a REPL command is a paren of degree 0.)

The degree of the paren is reflected in the length of the list of environments it contains. Degree-0 parens have no environments, degree-1 parens have exactly one, and so on. If we want to represent a degree-N expression, then the parens we use are limited in a specific way:

  <expr> ::= <s-expression where some leaves are <paren>>
  <paren> ::=
    (close <identifier>
      <for some (M < N), an M-element list of
        <environment of <expr>>)
  <paren> ::=
    (open-and-close <expr>
      <for some (M <= N), an M-element list of
        <environment of <expr>>)>
The (open-and-close ...) syntax begins a nested expression. The environments serve to fill the holes in the <expr>, resuming the previous level of nesting. Each element of the list fills holes of a different degree. Holes of degree higher than the number of environments in the list are not filled; they remain holes. For instance, in `(a b (c d ,e) f), the "(" before "c" has two holes in its expression (",e" and ") f"), but it only fills the hole for ") f". The hole for ",e" is a higher degree than the "(" paren, so it's not filled at such a local place. It's only filled by the "`" paren on the outside.

The (close ...) syntax begins a hole of degree equal to the number of elements of the list. The list of environments will be used when the hole is replaced with an expression. It'll fill in the (low-degree) holes of that expression.

Note that the list lengths correspond with the degrees of holes, but not with the degrees of expressions. In fact, a degree-N expression does not contain any expressions of degrees other than N. If we consider ourselves to be working with higher quasiquotations of an infinite degree N, but every (close ...) actually occurring in our data has finite degree, then we can represent our data using finite lists. We never need to select a finite value for N!


In Haskell, the strongly typed variations I wrote do require a finite value for N to be decided beforehand (and baked into the name of the type), because I'm pretty sure that vastly simplifies the type system features I would need to use to get it to work. :-p Roughly, the difficulty is that I need 0 to give me something of kind ( * ), 1 to give me something of kind ( * -> * ), 2 to give me something of kind (( * -> * ) -> ( * -> * )), and so on, so I would need kinds that depend on values. Agda or Idris might already be up for this task, but I doubt that's going to be the kind of effort I want to spend since I intended to build my macroexpander in (untyped) Racket to begin with.

There might just be a little more I want to tinker with in Haskell, because on my way to defining this data structure I started to develop some code for "higher monads," and it would be fun if this data structure turned out to be an instance of that concept. Still, at this point I'm probably ready to go back to Racket.

I'm even hopeful again that this macro system might play nicely with Racket's. Racket has some hygiene features[1] that walk recursively over the inputs and outputs of macros, expecting them to be s-expression-shaped with no holes. I wasn't sure that Racket's technique could be reconciled with higher quasiquotation. With this data structure, the exotic nesting of higher quasiquotations is converted to the traditional kind of nesting that Racket expects.

So, this might be a usable self-contained Racket library in the end -- not even a framework but a seamless library -- which is what I want, because that would make it easy to clarify the meaning of higher quasiquotation in terms of an existing ecosystem before I use it in Cene. :)

Since this thread and my code comments contain some walls of text, I'll see if I can convert them to a blog post soon.


[1] In particular, Racket uses a hygiene technique where it attaches a fresh scope label to a piece of syntax before macroexpanding and then flips the presence of that scope after macroexpanding so that the scope winds up attached to only the parts of the macro result that don't come from the input (making that region more local than the rest). Racket also has a "syntax taints" feature which lets macros attach "dye packs" to their results so that the identifiers occurring in those results can't be used by a client to access private module bindings.